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Lipschitz percolation

   
@article{ECP1521,
	author = {Nicolas Dirr and Patrick Dondl and Geoffrey Grimmett and Alexander Holroyd and Michael Scheutzow},
	title = {Lipschitz percolation},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {15},
	year = {2010},
	keywords = {percolation, Lipschitz embedding, random surface},
	abstract = {We prove the existence of a (random) Lipschitz function $F:\mathbb{Z}^{d-1}\to\mathbb{Z}^+$ such that, for every $x\in\mathbb{Z}^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\mathbb{Z}^{d}$. The Lipschitz constant may be taken to be $1$ when the parameter $p$ of the percolation model is sufficiently close to $1$.},
	pages = {no. 2, 14-21},
	issn = {1083-589X},
	doi = {10.1214/ECP.v15-1521},    
        url = {http://ecp.ejpecp.org/article/view/1521}}